Question

The first international chess tournament was held in London in 1851. This single-elimination tournament (in which paired competitors played matches and only the winner of a match continued to the next round) began with 16 competitors. How many matches were played?

Answer 1

Total number of matches played were 15

Explanation:

Data provided in the question:

Number of competitors = 16

The tournament is a single elimination tournament

paired competitors played matches and only the winner of a match continued to the next round

therefore,

Dividing 16 competitors in pairs, there will be 8 pairs.

as each pair plays 1 match

Thus,

8 matches ............(a)

Now,

winner of 8 matches will be 8 competitors

Further, dividing the 8 competitors in pairs, there will be 4 pairs.

as each pair plays 1 match

Thus,

4 matches ............(b)

Further, dividing the 4 competitors in pairs, there will be 2 pairs.

as each pair plays 1 match

Thus,

2 matches ............(c)

now, the winner of the 2 matches will be 2 competitors,

thus, 1 more match to decide the winner.

thus,

1 match .............(d)

adding (a), (b), (c) and (d)

we get

8 + 4 + 2 + 1 = 15 matches

Hence,

Total number of matches played were 15